More than a decade ago, when she was approaching the height of her considerable powers, and at 22 already talking about retirement, I sat down opposite Venus Williams and began an interview by asking her to recall how it all began, when did she first knew she was going to be a champion?

She looked at me, I remember, as she was apt to look at opponents across a net, half smiling, super-gracious, with a hint of a raised eyebrow as if to say "Is that all you've got?" And then she rehearsed what seemed a familiar story. It all started, she said, when she was three and a half years old, and her daddy took her down to the nearest club in Los Angeles, a lilywhite place, and set up a game for her against the resident men's pro. She was a bit nervous at first, she suggested, but after a while she was "serving overarm, aces and everything, hitting forehands down the line".

I recall picturing this scene as she embellished the detail of the story, her cornrow hair and cut-down racket, her daddy, Richard, standing on the sidelines and then I asked, inevitably, "And how did you do?"

Venus looked at me full face, eyes wide. "Well I was used to beating guys by then, so I beat this guy, too ..." she said. "Straight sets."

I looked down to check my tape recorder was running. "Really?" I said, "You beat him? When you were three and a half?"

The champion paused a beat, stared at me with incredulity, and erupted into her life-loving laugh: "Nahhhh!" she said. "Course I didn't!"

If recalling this sucker punch still makes me cringe, one of the comforting things about watching Venus and Serena, a feature-length documentary that goes on cinema release in time for Wimbledon fortnight, is to realise that if the sisters have enjoyed anything more than winning tennis matches, it is winding up gullible journalists. Another is the fact that Venus's tall story was not a million miles from the truth.

In some ways the sisters rise from the public courts of Compton, LA ("ghetto Cinderellas" as their father famously styled them) to more than a decade of domination in the women's game has been so often told that it has lost its edges of wild improbability. Having it set out again on film – with telling contributions from Bill Clinton, and Chris Rock and John McEnroe and Anna Wintour among others – serves to re-establish the fabulous couldn't-make-it-up quality of their story. At one point a coach who was invited to come and see Venus play against her sister on courts "strewn with broken glass", when they were still infants, recalls how, having hit the cover off a few hundred balls Venus asked her father if she could take a toilet break. She left the court, to the visitor's amazement, walking on her hands and, he recalls, as she did so, he whispered to her father: "I think you might have the next Michael Jordan there." Richard Williams responded, "No, I got the next two."

Only the very greatest athletes – Ali choosing the round he would end a fight, Babe Ruth pointing to the place in the stands where he would hit his home run – deal much in prophecy. That Richard Williams could predict the future for his daughters from the age of four and five as rival world No1s, and have it come true, is perhaps the most remarkable feat of sporting soothsaying of all. He is a natural scene-stealer, and he dominates the early part of this narrative, taking the cameras back to the broken down shack in Shreveport, Louisiana, where he grew up with his single mother. Finding the piece of waste ground where, as a teenager, "six or seven [white] men held me down and drove a cross-tie spike from a railroad into my leg because I wouldn't call them mister … when they called me nigger", he describes the act that effectively ended his own sporting ambitions, and saw them magnified in his extraordinary daughters. There follow one or two new insights into how his home-made programme for Venus and Serena was enforced, how he had them hurl rackets and footballs as far as they could to develop power, how he railed against an early interviewer, who, startled by Venus's conviction in her abilities, seemed to want to put a bit of doubt in her head.

One of the fascinating near-mythical aspects of the film and the story, though, is how the father, for all his controlling commitment, is not only overwhelmed by his all-powerful progeny, but increasingly by their mother, Oracene, who emerges, as the sisters grow, as their consistent guiding light. As Venus says at one point, Richard "provided the body of what we did, but Mom was always the spine". Oracene eventually divorced Richard having "put up with a lot" (not least the five children he had as part of "another family"); throughout she seems to instil in her daughters not only their indefatigable grace, but their refusal, ever, to take a step back (except occasionally for each other); they were, as she once memorably said, "to be nobody's Stepin Fetchit".

A few – embittered players, line judges, commentators, and crowds – have, as we are reminded here, sometimes tried to treat the sisters as such. They have almost always – despite a couple of ferocious lapses from Serena – responded with a mixture of unflinching competitiveness and last-laugh generosity. Few American sporting heroes, Ali included, have successfully negotiated so many divides, and come out smiling. As no doubt they will show in the coming tournament, they are not planning farewells any time soon: "At some point the star will fade," Serena says, "but I think we are just going to keep playing and playing."